US20110228927A1 - Cryptographic Method of Multilayer Diffusion in Multidimension - Google Patents
Cryptographic Method of Multilayer Diffusion in Multidimension Download PDFInfo
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- US20110228927A1 US20110228927A1 US12/726,833 US72683310A US2011228927A1 US 20110228927 A1 US20110228927 A1 US 20110228927A1 US 72683310 A US72683310 A US 72683310A US 2011228927 A1 US2011228927 A1 US 2011228927A1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
Definitions
- the invention relates to a cryptographic method. More particularly, the invention relates to a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), and further, repeating the diffusion function for at least one time to create a multilayer effect in order to perform the encryption and the decryption.
- a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext)
- a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext)
- repeating the diffusion function for at least one time to create a multilayer effect in order to perform the encryption and the decryption.
- the present invention emphasizes the multilayer effect of multidimensional diffusion.
- the diffusion function herein is notated specially by AF(p 1 , p 2 , . . . p n ) to differentiate from the traditional symbolization of matrix position.
- the invention provides a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), in which a multidimensional medium is meanwhile overlapped to the diffusion-area; accordingly, repeating the diffusion function for at least one time thus brings about the multilayer effect.
- a so called diffusion-cycle is then able to divide into two parts: one for encrypting, the other for decrypting; consequently, the original status of the diffusion-area is recovered through the diffusion-cycle.
- FIG. 1 is a summary flow chart diagram showing the main steps taken while encrypting/decrypting by repeating diffusion function in accordance with the present invention
- FIG. 2A is a summary flow chart diagram of FIG. 1 , 410 showing the steps taken while originating the function of point-diffusion from a diffusion-center in accordance with the present invention
- FIG. 2B is a two-dimension visualized diagram of FIG. 2A showing the point-diffusion by way of a medium anchoring to a diffusion-center in accordance with the present invention
- FIG. 3A is a summarized flow chart diagram of FIG. 1 , 420 showing the steps taken while originating the function of block-diffusion from a block diffusion-center in accordance with the present invention
- FIG. 3B is a two-dimension visualized diagram of FIG. 3A showing the block-diffusion by way of a medium anchoring to a diffusion-center, a block anchoring to the diffusion-center to form a block diffusion-center in accordance with the present invention.
- FIG. 1 shows an embodiment of the present invention in flow chart diagram form.
- This system comprises of: inputting a plaintext in encryption or a ciphertext in decryption 100 ; inputting a series of password data forward in encryption or backward in decryption 200 ; further, by the password data, converting the dimensions of the plaintext 300 , and implementing with a function of diffusion, repeated T E times in encryption, T D times in decryption 400 ; outputting the ciphertext in encryption or the plaintext in decryption 600 if completing all password data 500 .
- FIG. 2A shows an embodiment of the point-diffusion function, FIG. 1 , 410 , in flow chart diagram.
- the function comprises of: reading a diffusion-area (plaintext/ciphertext), a diffusion-center, and a medium with an anchor-point 201 ; anchoring the medium to the diffusion-center with the anchor-point 411 ; implementing the point-diffusion AF(p 1 , p 2 , . . . p n ) 412 , which is further detailed in Notation of Point-Diffusion.
- FIG. 2B with 2D visualization for a more clear view, the diffusion effect colored from white to black generates the column segments a-g, a-b for later diffusion calculation.
- A [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ]
- ⁇ S [ s 11 s 12 s 13 s 14 s 21 s 22 s 23 s 24 s 31 s 32 s 33 s 34 s 41 s 42 s 43 s 44 ] , ⁇ S .
- a y ⁇ ( 2 ) [ a 12 a 22 a 32 a 42 ]
- a y ⁇ ( 3 ) [ a 13 a 23 a 33 a 43 ]
- ⁇ S [ s 111 s 121 s 131 a 141 a 211 a 221 a
- Ax 3 expresses a series of two dimensional binary matrixes A x on the axis x; wherein Ax 3 comprises
- Ay 2 expresses a series of two dimensional binary matrixes A y on the axis y; wherein Ay 2 comprises
- Az 1 expresses a series of two dimensional binary matrixes A z on the axis z; wherein Az 1 comprises
- a z ⁇ ( 1 ) [ a 111 a 121 a 131 a 141 a 211 a 221 a 231 a 241 a 311 a 321 a 331 a 341 a 411 a 421 a 431 a 441 ]
- a z ⁇ ( 2 ) [ a 112 a 122 a 132 a 142 a 212 a 222 a 232 a 242 a 312 a 322 a 332 a 342 a 412 a 422 a 432 a 442 ]
- a z ⁇ ( 0 ) [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
- FIG. 3A shows an embodiment of the block-diffusion function, FIG. 1 , 420 , in flow chart diagram.
- the function comprises of: reading a diffusion-area (plaintext/ciphertext), a diffusion-center, a medium with an anchor-point and a block with an anchor-point 202 ; anchoring the medium and the block to the diffusion-center with the anchor-point 421 ; implementing the block-diffusion ⁇ F( ⁇ circumflex over (p) ⁇ 1 , ⁇ circumflex over (p) ⁇ 2 , . . . ⁇ circumflex over (p) ⁇ n ) 422 , further detailed in Notation of Block-Diffusion.
- FIG. 3B with 2D visualization for a more clear view, the diffusion effect colored from white to black generates the block-column segments a-c, a-b for later diffusion calculation.
- a ⁇ ⁇ F ⁇ ( p ⁇ 1 , p ⁇ 2 , ... ⁇ , p ⁇ n ) A ⁇ ⁇ A ⁇ ⁇ d ⁇ 1 ⁇ p ⁇ ⁇ A ⁇ ⁇ d ⁇ 2 ⁇ p ⁇ ⁇ ... ⁇ A ⁇ ⁇ d ⁇ n ⁇ p ⁇ ⁇ S ;
- a ⁇ ⁇ d ⁇ i ⁇ p ⁇ [ A ⁇ d ⁇ i ⁇ ( 2 ) , ... ⁇ , A ⁇ d ⁇ i ⁇ ( p ⁇ i ) , A ⁇ d ⁇ i ⁇ ( 0 ) , A ⁇ d ⁇ i ⁇ ( p ⁇ i ) , ... ⁇ , A ⁇ d ⁇ i ⁇ ( d ⁇ i - 1 ) ] ;
- A [ a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ]
- S [ s 11 s 12 s 13 s 14 s 21 s 22 s 23 s 24 s 31 s 32 s 33 s 34 s 41 s 42 s 43 s 44 ]
- ⁇ B [ b 11 b 12 b 21 b 22 ]
- S . ( 2 , 1 )
- B . ( 1 , 1 ) ;
- ⁇ circumflex over (x) ⁇ 2 expresses a series of one dimensional binary matrixes ⁇ ⁇ circumflex over (x) ⁇ on the axis ⁇ circumflex over (x) ⁇ ; wherein ⁇ circumflex over (x) ⁇ 2 comprises
- a ⁇ x ⁇ ⁇ ( 2 ) [ a 31 a 32 a 33 a 34 a 41 a 42 a 43 a 44 ]
- a ⁇ x ⁇ ⁇ ( 0 ) [ 0 0 0 0 0 0 0 0 ]
- ⁇ 2 expresses a series of one dimensional binary matrixes ⁇ ⁇ on the axis ⁇ ; wherein ⁇ 2 comprises
- a ⁇ y ⁇ ⁇ ( 2 ) [ a 12 a 13 a 22 a 23 a 32 a 33 a 42 a 43 ]
- a ⁇ y ⁇ ⁇ ( 0 ) [ 0 0 0 0 0 0 0 0 ]
- ⁇ S [ s 111 s 121 s 131 s 141 s 211 s 221 s 231 a
- ⁇ circumflex over (x) ⁇ 2 expresses a series of two dimensional binary matrixes ⁇ ⁇ circumflex over (x) ⁇ on the axis ⁇ circumflex over (x) ⁇ ; wherein ⁇ circumflex over (x) ⁇ 2 comprises
- ⁇ 2 expresses a series of two dimensional binary matrixes ⁇ on the axis ⁇ ; wherein ⁇ 2 comprises ⁇ (2) to positions 1, 3 is equal to
- ⁇ circumflex over (z) ⁇ 1 expresses a series of two dimensional binary matrixes ⁇ circumflex over (z) ⁇ on the axis ⁇ circumflex over (z) ⁇ ; wherein ⁇ circumflex over (z) ⁇ 1 comprises
- a ⁇ z ⁇ ⁇ ( 0 ) [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
- a password “Yourlips”, its ASCII code is 59 6f 75 72 6c 69 70 73.
- ASCII code first, excludes the last digit 3; second, forms into octal format 26 26 75.65 34 46 61 51 34 07; third, adds 1 to each digit; Table 1-2 shows that the password includes 10 diffusion-centers.
- Table 1-1 overlap for 8 times to shape a 8 ⁇ 8 ⁇ 8 binary matrix, shown as a 8 ⁇ 8 matrix in ASCII code format as in Table 2-1.
- Table 2-1 the row stands for a x-y plane, namely Table 1-1, and all rows resolve as the axis z.
- a password “YourlipsY”, its ASCII code is 59 6f 75 72 6c 69 70 73 59.
- ASCII code first, subtracts 8 if a digit >7 and leaves 51 67 75 72 64 61 70 73 51; second, every three-digit forms a division; third, adds 1 to each digit; Table 2-2 shows that the password includes 6 diffusion-centers.
- Table 2-1 means a x-y plane
- it can be figured out by the 3D scheme through rearranging every plane then placing to the corresponding row of 2D table, as Ax 6 and Ay 2 as follows.
- ⁇ ⁇ plane ⁇ ⁇ of ⁇ ⁇ Ax 6 [ 10110001 01111010 01110100 10001001 11111111 00000000 11111111 11111111 ]
- ⁇ Ax 6 [ d ⁇ ⁇ 9 d ⁇ ⁇ 6 d ⁇ ⁇ 7 d ⁇ ⁇ 7 da d ⁇ ⁇ 4 d ⁇ ⁇ 2 d ⁇ ⁇ 9 d ⁇ ⁇ 9 d ⁇ ⁇ 6 d ⁇ ⁇ 7 d ⁇ ⁇ 7 da d ⁇ ⁇ 4 d ⁇ ⁇ 2 d ⁇ ⁇ 9 d ⁇ ⁇ 9 d ⁇ ⁇ 6 d ⁇ ⁇ 7 d ⁇ ⁇ 7 da d ⁇ ⁇ 4 d ⁇ ⁇ 2 d ⁇ ⁇ 9 d ⁇ ⁇ 9 d ⁇ ⁇ 6 d ⁇ ⁇ 7 d ⁇ ⁇ 7 da d ⁇ ⁇ 4 d ⁇ ⁇ 2 d ⁇ ⁇ 9
- a 5 [ c ⁇ ⁇ 4 11 3 ⁇ a b ⁇ ⁇ 7 7 ⁇ a 64 01 ed 8 ⁇ f c ⁇ ⁇ 0 8 ⁇ e 8 ⁇ d a ⁇ ⁇ 1 b ⁇ ⁇ 7 cb 00 53 9 ⁇ c 48 26 ee eb 8 ⁇ b 23 5 ⁇ b 5 ⁇ b 27 47 91 b ⁇ ⁇ 1 5 ⁇ c cb b ⁇ ⁇ 8 34 67 4 ⁇ a 9 ⁇ f b ⁇ ⁇ 3 74 4 ⁇ c 92 17 5 ⁇ d 5 ⁇ a 7 ⁇ e 7 ⁇ d 84 0 ⁇ f a ⁇ ⁇ 0 19
- a 6 14 [ 24 31 7 ⁇ d 3 ⁇ a e ⁇ ⁇ 8 fb 8 ⁇ d c ⁇ ⁇ 1 93 3 ⁇ d 8 ⁇ b 10 a ⁇ ⁇ 1 6 ⁇ a 61 21 a ⁇ ⁇ 6 25 c ⁇ ⁇ 6 86 ee 81 d ⁇ ⁇ 0 4 ⁇ a 47 39 33 b ⁇ ⁇ 3 91 10 71 50 ⁇ 50 0 ⁇ f 15 63 9 ⁇ f 62 25 ee c ⁇ ⁇ 6 87 9 ⁇ c e ⁇ ⁇ 2 7 ⁇ e 0 ⁇ a 9 ⁇ d 28 9 ⁇ f ce c ⁇
Abstract
The invention provides a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), in which a multidimensional medium is meanwhile overlapped to the diffusion-area; accordingly, repeating the diffusion function for at least one time thus brings about the multilayer effect. FIG. 1 shows an embodiment of the present invention in flow chart diagram form, comprising of: inputting a plaintext in encryption or a ciphertext in decryption 100; inputting a series of password data forward in encryption or backward in decryption 200; further, by the password data, converting the dimensions of the plaintext 300, and implementing with a diffusion function, repeated TE times in encryption, TD times in decryption 400; outputting the ciphertext in encryption or the plaintext in decryption 600 if completing all password data 500.
Description
- The Applicant's following patent applications are related to the invention and are incorporated herein by reference: “Diffused Data Encryption/Decryption Processing Method”, application Ser. No. 12/365,160, filed Feb. 3, 2009 (CIP of application Ser. No. 10/963,014, filed Oct. 12, 2004); “Multipoint Synchronous Diffused Encryption/Decryption Method”, application Ser. No. 11/171,549, filed Jun. 30, 2005.
- 1. Field of the Invention
- The invention relates to a cryptographic method. More particularly, the invention relates to a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), and further, repeating the diffusion function for at least one time to create a multilayer effect in order to perform the encryption and the decryption.
- 2. Description of the Related Art
- The prior art described that the coding of a 2D diffusion-area, see application Ser. No. 12/365,160, page 7, teaches the math of A(i, j)=A⊕Aci⊕Arj⊕b(i, j); further expressed the status of diffusion from inward to outward or vice versa in reverse, and implemented to multidimensional matrix A(i1, i2, . . . in), see application Ser. No. 11/171,549, page 4, 7.
- The present invention emphasizes the multilayer effect of multidimensional diffusion. The diffusion function herein is notated specially by AF(p1, p2, . . . pn) to differentiate from the traditional symbolization of matrix position.
- The invention provides a diffusion function working on a multidimensional diffusion-area (plaintext/ciphertext), in which a multidimensional medium is meanwhile overlapped to the diffusion-area; accordingly, repeating the diffusion function for at least one time thus brings about the multilayer effect. In addition, the numbers of repetition, a so called diffusion-cycle, is then able to divide into two parts: one for encrypting, the other for decrypting; consequently, the original status of the diffusion-area is recovered through the diffusion-cycle. The steps are shown as follows:
-
- (a) Selecting a diffusion function, a multidimensional medium;
- (b) Inputting a multidimensional diffusion-area (plaintext/ciphertext), for which the dimensions are the same as the medium's, and generating a diffusion-cycle;
- (c) Repeating the diffusion function working on a plaintext for a first part of the diffusion-cycle to generate a ciphertext;
- (d) Repeating the diffusion function working on the ciphertext for a second part of the diffusion-cycle to recover the plaintext.
-
FIG. 1 is a summary flow chart diagram showing the main steps taken while encrypting/decrypting by repeating diffusion function in accordance with the present invention; -
FIG. 2A is a summary flow chart diagram ofFIG. 1 , 410 showing the steps taken while originating the function of point-diffusion from a diffusion-center in accordance with the present invention; -
FIG. 2B is a two-dimension visualized diagram ofFIG. 2A showing the point-diffusion by way of a medium anchoring to a diffusion-center in accordance with the present invention; -
FIG. 3A is a summarized flow chart diagram ofFIG. 1 , 420 showing the steps taken while originating the function of block-diffusion from a block diffusion-center in accordance with the present invention; -
FIG. 3B is a two-dimension visualized diagram ofFIG. 3A showing the block-diffusion by way of a medium anchoring to a diffusion-center, a block anchoring to the diffusion-center to form a block diffusion-center in accordance with the present invention. -
FIG. 1 shows an embodiment of the present invention in flow chart diagram form. This system comprises of: inputting a plaintext in encryption or a ciphertext indecryption 100; inputting a series of password data forward in encryption or backward indecryption 200; further, by the password data, converting the dimensions of theplaintext 300, and implementing with a function of diffusion, repeated TE times in encryption, TD times indecryption 400; outputting the ciphertext in encryption or the plaintext indecryption 600 if completing allpassword data 500. -
FIG. 2A shows an embodiment of the point-diffusion function,FIG. 1 , 410, in flow chart diagram. The function comprises of: reading a diffusion-area (plaintext/ciphertext), a diffusion-center, and a medium with an anchor-point 201; anchoring the medium to the diffusion-center with the anchor-point 411; implementing the point-diffusion AF(p1, p2, . . . pn) 412, which is further detailed in Notation of Point-Diffusion. In addition, also seeFIG. 2B with 2D visualization for a more clear view, the diffusion effect colored from white to black generates the column segments a-g, a-b for later diffusion calculation. -
- A: a diffusion-area, wherein A expresses a d1×d2× . . . ×dn binary matrix, wherein A includes a diffusion-center {dot over (P)} expressed (p1, p2, . . . pn) coordinate position.
- S: a n-dimension medium, expresses a s1×s2× . . . ×sn binary matrix, wherein S includes an anchor-point {dot over (S)} expressed (s1, s2, . . . , sn) coordinate position.
- AF(p1, p2, . . . pn): the diffusion-area A performs the function of point-diffusion at position {dot over (P)}, wherein S overlaps A by {dot over (S)} anchoring to {dot over (P)}; further comprising:
- AF(p1, p2, . . . , pn)=A⊕Ad1p⊕Ad2p⊕ . . . ⊕Adnp⊕S;
- Adip=[Ad
i (2), . . . , Adi (pi), Adi (0), Adi (pi), . . . , Adi (di−1)]; - Adip expresses a series of n−1 dimensional binary matrix Ad
i the axis di. Furthermore, Adi (pi) represents the original Adi the coordinate pi, and then, Adi (0) expresses a zero matrix filling at the coordinate pi. - For example: 2D point-diffusion, with rows for x, columns for y, AF(px=3, py=2).
- Suppose
-
- In detail, Ax3 expresses a series of one dimensional binary matrixes Ax on the axis x; wherein Ax3 comprises Ax (2)=[a21 a22 a23 a24] to position 1, Ax (3)=[a31 a32 a33 a34] to positions 2, 4, and Ax (0)=[0 0 0 0] at position 3. Furthermore, Ay2 expresses a series of one dimensional binary matrixes Ay on the axis y; wherein Ay2 comprises
-
- to positions 1, 3,
-
- to position 4, and
-
- at position 2.
Finally, the effective S comes from the overlap between S and A, while {dot over (S)}=(2,1) anchors to P=(3,2).
For example: 3D point-diffusion AF(px=3, py=2, pz=1). Suppose -
- In detail, Ax3 expresses a series of two dimensional binary matrixes Ax on the axis x; wherein Ax3 comprises
-
- to
position 1. -
- to positions 2, 4, and
-
- at position 3.
Furthermore, Ay2 expresses a series of two dimensional binary matrixes Ay on the axis y; wherein Ay2 comprises -
- to
positions 1, 3, -
- to position 4, and
-
- at position 2.
Moreover, Az1 expresses a series of two dimensional binary matrixes Az on the axis z; wherein Az1 comprises -
- to position 2,
-
- to position 3, and
-
- at
position 1. Finally, the effective S comes from the overlap between S and A, while {dot over (S)}=(2,1,3) anchors to P=(3,2,1). - AF(p1, p2 t, . . . , pn): A performs the function of point-diffusion, repeated t times.
- Example: (a) AF(p1, p2 2, . . . , pn)=AF(p1, p2, . . . , pn)F(p1, p2, . . . , pn)
- (b) AF(p1, p2 1, . . . , pn)=AF(p1, p2, . . . , pn)
- (c) AF(p1, p2 0, . . . , pn)=A
- Example: (a) AF(p1, p2 2, . . . , pn)=AF(p1, p2, . . . , pn)F(p1, p2, . . . , pn)
- T: a diffusion-cycle, expresses AF(p1, p2 T, . . . , pn)=A, wherein T=2U+1, U=┌log2 u┐, u=max(d1, d2, . . . , dn).
-
FIG. 3A shows an embodiment of the block-diffusion function,FIG. 1 , 420, in flow chart diagram. The function comprises of: reading a diffusion-area (plaintext/ciphertext), a diffusion-center, a medium with an anchor-point and a block with an anchor-point 202; anchoring the medium and the block to the diffusion-center with the anchor-point 421; implementing the block-diffusion ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n) 422, further detailed in Notation of Block-Diffusion. In addition, also seeFIG. 3B with 2D visualization for a more clear view, the diffusion effect colored from white to black generates the block-column segments a-c, a-b for later diffusion calculation. -
- A: a n-dimension plaintext, expresses a d1×d2× . . . ×dn binary matrix, wherein A includes a diffusion-center P expressed (p1, p2, . . . pn) coordinate position.
- S: a n-dimension medium, expresses a s1×s2× . . . ×sn binary matrix, wherein S includes an anchor-point {dot over (S)} expressed ({dot over (s)}1, {dot over (s)}2, . . . , {dot over (s)}n) coordinate position.
- B: a n-dimension unit-block, expresses a b1×b2× . . . ×bn binary matrix, wherein B includes an anchor-point {dot over (B)} expressed ({dot over (b)}1, {dot over (b)}2, . . . , {dot over (b)}n) coordinate position.
- ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n):  performs the function of block-diffusion, wherein  expresses A by B unit seeing that {dot over (B)} anchors to P, and thus, includes a block diffusion-center {circumflex over (P)} expressed ({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n) coordinate position. Therefore, A translates into a {circumflex over (d)}1×{circumflex over (d)}2× . . . ×{circumflex over (d)}n binary matrix, wherein {circumflex over (d)}i=┌(pi−{dot over (b)}i)/bi┐+┌(di−pi+{dot over (b)}i┐, and {circumflex over (p)}i=(pi−{dot over (b)}i)/bi|+1; further comprising:
-
- Â{circumflex over (d)}i{circumflex over (p)} expresses a series of n−1 dimensional binary matrixes
-
- on the axis {circumflex over (d)}i. Furthermore,
-
- represents the original
-
- at the coordinate {circumflex over (p)}i, and then,
-
- expresses a zero matrix tilling at the coordinate {circumflex over (p)}i.
-
- For example: 2D block-diffusion, with rows for x, columns for y, AF(px=3, py=2). Suppose
-
- thus, dimensions {circumflex over (x)}=┌(3−1)/2┐+┌(4−3+1)/2┐=2 and ŷ=┌(2−1)/2┐+┌(4−2+1)/2┐=3;
- that shows the block-diffusion in 2×3 blocks, but with the data still kept in 4×4 bits. And now {circumflex over (p)}x=┌(3−1)/2┐+1=2, {circumflex over (p)}y=┌(2−1)/2┐+1=2, thus
- In detail, Â{circumflex over (x)}2 expresses a series of one dimensional binary matrixes Â{circumflex over (x)} on the axis {circumflex over (x)}; wherein Â{circumflex over (x)}2 comprises
-
- to
position 1, and -
- at position 2. Furthermore, Âŷ2 expresses a series of one dimensional binary matrixes Âŷ on the axis ŷ; wherein Âŷ2 comprises
-
- to
positions 1, 3, and -
- at position 2. Finally, the effective S comes from the overlap between S and A, while {dot over (S)}=(2,1) anchors to P=(3,2).
-
- For example: 3D block-diffusion AF(px=3, py=2, pz=1). Suppose
-
- thus, dimensions {circumflex over (x)}=┌(3−1)/2┐+┌(4−3+1)/2┐=2, ŷ=┌(2−1)/2┐+┌(4−2+1)/2┐=3, and {circumflex over (z)}=┌(1−1)/2┐+┌(4−1+1)/2┐=2; further
-
- that shows the block-diffusion in 2×3×2 blocks, but with the data still kept in 4×4×3 bits. And now {circumflex over (p)}x=┌(3−1)/2┐+1=2, {circumflex over (p)}y=┌(2−1)/2┐+1=2, {circumflex over (p)}z=┌(1−1)/2┐+1=1, thus,
- In detail, Â{circumflex over (x)}2 expresses a series of two dimensional binary matrixes Â{circumflex over (x)} on the axis {circumflex over (x)}; wherein Â{circumflex over (x)}2 comprises
-
- to
position 1, and -
- at position 2.
Furthermore, Âŷ2 expresses a series of two dimensional binary matrixes Âŷ on the axis ŷ; wherein Âŷ2 comprises Âŷ(2) topositions 1, 3 is equal to -
- at position 2.
Moreover, Â{circumflex over (z)}1 expresses a series of two dimensional binary matrixes Â{circumflex over (z)} on the axis {circumflex over (z)}; wherein Â{circumflex over (z)}1 comprises -
- to position
-
- at
position 1. Finally, the effective S comes from the overlap between S and A, while {dot over (S)}=(2,1,3) anchors to P=(3,2,1). - ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . , {dot over (p)}n): Â performs the function of block-diffusion, repeated t times.
- Example: (a) ÂF({circumflex over (p)}1, {circumflex over (p)}2 2, . . . , {circumflex over (p)}n)=ÂF({circumflex over (p)}i, {circumflex over (p)}2, . . . , {dot over (p)}n)F({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n)
- (b) {dot over (A)}F({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n)=ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n)
- (c) ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n)=A
- Example: (a) ÂF({circumflex over (p)}1, {circumflex over (p)}2 2, . . . , {circumflex over (p)}n)=ÂF({circumflex over (p)}i, {circumflex over (p)}2, . . . , {dot over (p)}n)F({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n)
- T: a diffusion-cycle, expresses {dot over (A)}F({circumflex over (p)}1, {circumflex over (p)}2 T, . . . {dot over (p)}n)=A, wherein T=2U+1, U=┌log2 u┌, u=max(┌di/bi┐, 1≦i≦n).
- To make it easier to understand the content of the present invention, examples in detail are described as follows:
- Suppose a plaintext A: “smoother”, its ASCII code is 73 6d 6f 6f 74 68 65 72, the binary format is shown as an 8×8 two-dimensional matrix as in Table 1-1.
-
TABLE 1-1 ASCII 73 6d 6f 6f 74 68 65 72 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 - Suppose a password: “Yourlips”, its ASCII code is 59 6f 75 72 6c 69 70 73. For applying to the plaintext, the ASCII code: first, excludes the last digit 3; second, forms into octal format 26 26 75.65 34 46 61 51 34 07; third, adds 1 to each digit; Table 1-2 shows that the password includes 10 diffusion-centers.
-
TABLE 1-2 ASCII 26 26 75 65 34 46 61 51 34 07 Row 3 3 8 7 4 5 7 6 4 1 Column 7 7 6 6 5 7 2 2 5 8 - Supposes
-
- reads every diffusion-center in order, if from 1 to 10 on encryption, then from 10 back to 1 on decryption; counts the diffusion-cycle T=23+1=16, if 1 time on encryption, then 15 times on decryption. In math, inputs the plaintext A, then runs A1, A1 1, . . . A9 1 and outputs A1, A2, . . . A10 during encryption; inputs the ciphertext A10, then runs A10 15, A9 15, . . . A1 15 and outputs A9, . . . , A1, A during decryption. The details on the
order 1, 5, 10 are shown as below, Adi (0) marked in boldface. -
-
- Encryption at the 10th Diffusion-Center (1,8):
-
- Decryption at the 10th Diffusion-Center (1,8):
-
- Decryption at the 5th Diffusion-Center (4,5):
-
- Decryption at the 1st Diffusion-Center (3,7):
-
- Supposes that
-
- reads
every diffusion-center in order, if from 1 to 10 on encryption, then from 10 back to 1 on decryption; counts the diffusion-cycle T=22+1=8, since di/bi=4=22, and if 1 time on encryption, then 7 times on decryption. In math, inputs the plaintext A, then runs Â1, Â1 1, . . . Â9 1, and outputs A1, A2, . . . A10 during encryption; inputs the ciphertext A10, then runs Â10 7, Â9 7, . . . Â1 7 and outputs A9, . . . , A1, A during decryption. The details on theorder 1, 5, 10 are shown as below, -
- marked in boldface.
-
-
- Encryption at the 10th Diffusion-Center (1,8): (0, Zero in Aŷ, (5), 2nd Col.)
-
-
- Decryption at the 5th diffusion-center (4,5):
-
-
- Supposes
-
- selects a switch set Y=[1011011101]; reads every diffusion-center and Y element in order, if from 1 to 10 on encryption, then from 10 back to 1 on decryption; counts the diffusion-cycle, if Y element is 1, then T=23+1=16 with point-diffusion, otherwise, T=22+1=8 with block-diffusion, and if 1 time on encryption, then 15 or 7 times on decryption.
- In math, inputs the plaintext A, then runs A1, Â1 1, A2 1, A3 1, Â4 1, A5 1, A6 1, A7 1, Â8 1, A9 1 and outputs A1, A2, . . . , A9, A10 during encryption; inputs the ciphertext A10, then runs A10 15, Â9 7, A8 15, A7 15, A6 15, Â5 7, A4 15, A3 15, Â2 7, A1 15 and outputs A9, A8, . . . , A1, A during decryption. The details on the
order 1, 5, 10 are shown as below, Adi (0) and -
- marked in boldface.
-
-
-
-
-
-
- Supposes a plaintext A: let Table 1-1 overlap for 8 times to shape a 8×8×8 binary matrix, shown as a 8×8 matrix in ASCII code format as in Table 2-1. To figure out the later 3D calculation clearly with Table 2-1, the row stands for a x-y plane, namely Table 1-1, and all rows resolve as the axis z.
-
TABLE 2-1 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 73 6d 6f 6f 74 68 65 72 - Suppose a password: “YourlipsY”, its ASCII code is 59 6f 75 72 6c 69 70 73 59. For applying to the plaintext, the ASCII code: first, subtracts 8 if a digit >7 and leaves 51 67 75 72 64 61 70 73 51; second, every three-digit forms a division; third, adds 1 to each digit; Table 2-2 shows that the password includes 6 diffusion-centers.
-
TABLE 2-2 ASCII 516 775 726 461 707 351 First Dimension 6 8 8 5 8 4 Second Dimension 2 8 3 7 1 6 Third Dimension 7 6 7 2 8 2 - Supposes S1×1×1=1, {dot over (S)}=(1,1,1); reads every diffusion-center in order, if from 1 to 6 on encryption, then from 6 back to 1 on decryption; counts the diffusion-cycle T=23+1=16, if 1 time on encryption, then 15 times on decryption. In math, inputs the plaintext A, then runs A1, A1 1, . . . A5 1 and outputs A1, A2, . . . A6 during encryption; inputs the ciphertext A6, then runs A6 15, A5 15, . . . A1 15 and outputs A5, . . . , A1, A during decryption. The details on the
order 1, 6 are shown as below, Adi (0) marked in boldface. -
A 1 =AF(6,2,7)=A⊕Ax 6 ⊕Ay 2 ⊕Az 7 ⊕S=A 1; - Considering that the row of Table 2-1 means a x-y plane, it can be figured out by the 3D scheme through rearranging every plane then placing to the corresponding row of 2D table, as Ax6 and Ay2 as follows.
-
- In addition, S is anchored to position (6,2,7), see below,
value 1 found at px=6, py=2 on the 7th plane (pz=7). -
-
-
-
- In summation of the above description, the present invention herein complies with the constitutional, statutory, regulatory and treaty, patent application requirements and is herewith submitted for patent application. However, the description and its accompanied drawings are used for describing preferred embodiments of the present invention, and it is to be understood that the invention is not limited thereto. To the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures.
Claims (10)
1. A cryptographic method, including a plaintext M run by at least one variable module, each comprising of:
selecting dimensions of M, wherein M forms a d1×d2× . . . ×dn n-dimension binary matrix;
selecting a diffusion-center P, wherein P expresses a (p1, p2, . . . pn) n-dimension position;
selecting a medium S, wherein S is a s1×s2× . . . ×sn n-dimension binary matrix which has an anchor-point {dot over (S)}, wherein {dot over (S)} expresses a ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) n-dimension position;
selecting a function of point-diffusion AF(p1, p2, . . . , pn), wherein AF(p1, p2, . . . , pn)=A⊕Ad1p⊕Ad2p⊕ . . . ⊕Adnp⊕S;
setting a diffusion-cycle T, wherein T=2U+1, U=┌log2 u┐, and u=max(d1, d2, . . . , dn); letting T=TE+TD;
further, comprising steps of:
(a) encrypting M, wherein A=M; a ciphertext C=AF(p1, p2 T E , . . . , pn);
(b) decrypting C, wherein A=C; M=AF(p1, p2 T D , . . . , pn).
2. The cryptographic method according to claim 1 , wherein said function of point-diffusion comprises that:
S overlaps A, {dot over (S)} anchoring to P;
Adip, 1≦i≦n, expresses a series of n−1 dimensional binary matrixes Ad i , Adip=[Ad i (2), . . . , Ad i (pi), Ad i (0), Ad i (pi), . . . , Ad i (di−1)], on di axis in order, wherein Ad i (pi) represents the original matrix at pi position, and Ad i (0), expresses a zero matrix filling at pi position.
3. The cryptographic method according to claim 1 , further including a password, wherein said password has at least one variable data, said data read by said module, each including: (p1, p2, . . . , pn) and/or d1×d2× . . . ×dn and/or ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) and/or s1×s2× . . . ×sn and/or S and/or TE and/or TD.
4. A cryptographic method, including a plaintext M run by at least one variable module, each comprising of:
selecting dimensions of M, wherein M forms a d1×d2× . . . ×dn n-dimension binary matrix;
selecting a diffusion-center P, wherein P expresses a (p1, p2, . . . pn) n-dimension position;
selecting a medium S, wherein S is a s1×s2× . . . ×sn n-dimension binary matrix which has an anchor-point {dot over (S)}, wherein {dot over (S)} expresses a ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) n-dimension position;
selecting a block B, wherein B is a b1×b2× . . . ×bn n-dimension binary matrix which has an anchor-point {circumflex over (B)}, wherein {dot over (B)} expresses a ({dot over (b)}1, {dot over (b)}2, . . . , {dot over (b)}n) n-dimension position;
selecting a function of block-diffusion ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n), wherein ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n)=Â⊕Â{circumflex over (d)}1{circumflex over (p)}⊕Â{circumflex over (d)}2{circumflex over (p)}⊕ . . . ⊕A{circumflex over (d)}n{circumflex over (p)}⊕S;
setting a diffusion-cycle T, wherein T=2U+1, U=┌log2 u┐, and u=max(┌di/bi┐, 1≦i≦n); letting T=TE+TD;
further, comprising steps of:
(a) encrypting M, wherein Â=M; a ciphertext C=ÂF({circumflex over (p)}1, {circumflex over (p)}2 T E , . . . , {circumflex over (p)}n);
(b) decrypting C, wherein Â=C; M=ÂF({circumflex over (p)}1, {circumflex over (p)}2 T D , . . . , {circumflex over (p)}n).
5. The cryptographic method according to claim 4 , wherein said function of block-diffusion comprises that:
S overlaps A based on {dot over (S)} anchoring to P;
 expresses A by B unit based on {dot over (B)} anchoring to P, wherein  is {circumflex over (d)}1×{circumflex over (d)}2× . . . ×{circumflex over (d)}n n-dimension binary matrix which has a block diffusion-center {circumflex over (P)}, wherein {circumflex over (P)} expresses a ({circumflex over (p)}1, {circumflex over (p)}2, . . . {circumflex over (p)}n) n-dimension position; lets {circumflex over (d)}i=┌(pi−{dot over (b)}i)/bi┐+┌(di−pi+{dot over (b)}i)/bi┌, and {circumflex over (p)}i=┌(pi−{dot over (b)}i)/bi┐+1, 1≦i≦n;
Â{circumflex over (d)}i{circumflex over (p)}, 1≦i≦n, expresses a series of n−1 dimensional binary matrixes
on {circumflex over (d)}i axis in order, wherein
represents the original matrix at {circumflex over (p)}i position, and
expresses a zero matrix filling at {circumflex over (p)}i position.
6. The cryptographic method according to claim 4 , further including a password, wherein said password has at least one variable data, said data read by said module, each including: (p1, p2, . . . , pn) and/or d1×d2× . . . ×dn and/or ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) and/or s1×s2× . . . ×sn and/or S and/or ({dot over (b)}1, {dot over (b)}2, . . . , {dot over (b)}n) and/or b1×b2× . . . ×bn and/or TE and/or TD.
7. A cryptographic method, including a plaintext M run by at least one variable module, each comprising of:
selecting dimensions of M, wherein M forms a d1×d2× . . . ×dn n-dimension binary matrix;
selecting a diffusion-center P, wherein P expresses a (p1, p2, . . . pn) n-dimension position;
selecting a medium S, wherein S is a s1×s2× . . . ×sn n-dimension binary matrix which has an anchor-point {dot over (S)}, wherein {dot over (S)} expresses a ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) n-dimension position;
selecting a block B, wherein B is a b1×b2× . . . ×bn n-dimension binary matrix which has an anchor-point {dot over (B)}, wherein {dot over (B)} expresses a ({dot over (b)}1, {dot over (b)}2, . . . , {dot over (b)}n) n-dimension position;
selecting a switch Y, wherein Y represents a first value for a function of point-diffusion, a second value for a function of block-diffusion;
selecting said function of point-diffusion AF(p1, p2, . . . , pn), wherein AF(p1, p2, . . . , pn)=A⊕Ad1p⊕Ad2p⊕ . . . ⊕Adnp⊕S;
selecting said function of block-diffusion ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n), wherein ÂF({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n)=Â⊕Â{circumflex over (d)}1{circumflex over (p)}⊕Â{circumflex over (d)}2{circumflex over (p)}⊕ . . . ⊕Â{circumflex over (d)}n{circumflex over (p)}⊕S;
setting a diffusion-cycle T1, wherein T1=2U+1, U=┌log2 u┐, and u=max(d1, d2, . . . , dn); letting T1=TE1 TD1;
setting a diffusion-cycle T2, wherein T2=2U+1, U=┌log2 u┐, and u=max(┌di/bi┐, 1=i≦n); letting T2=TE2 TD2;
further, comprising steps of:
(a) encrypting M, wherein A=M; if Y equals to said first value, then a ciphertext C=AF(p1, p2 T E1 , . . . , pn); or if Y equals to said second value, then C=ÂF({circumflex over (p)}1, {circumflex over (p)}2 T E2 , . . . , {circumflex over (p)}n);
(b) decrypting C, wherein A=C; if Y equals to said first value, then M=AF(p1, p2 T D1 , . . . , pn); or if Y equals to said second value, then M=ÂF({circumflex over (p)}1, {circumflex over (p)}2 T D2 , . . . , {circumflex over (p)}n).
8. The cryptographic method according to claim 7 , wherein said function of point-diffusion comprises that:
S overlaps A, {dot over (S)} anchoring to P;
Adip, 1≦i≦n, expresses a series of n−1 dimensional binary matrixes Ad i , Adip=[Ad i (2), . . . , Ad i (pi), Ad i (0), Ad i (pi), . . . , Ad i (di−1)], on di axis in order, wherein Ad i (pi) represents the original matrix at pi position, and Ad i (0) expresses a zero matrix filling at pi position.
9. The cryptographic method according to claim 7 , wherein said function of block-diffusion comprises that:
S overlaps A based on {dot over (S)} anchoring to P;
 expresses A by B unit based on {dot over (B)} anchoring to P, wherein  is {circumflex over (d)}1×{circumflex over (d)}2× . . . ×{circumflex over (d)}n n-dimension binary matrix which has a block diffusion-center {circumflex over (P)}, wherein {circumflex over (P)} expresses a ({circumflex over (p)}1, {circumflex over (p)}2, . . . , {circumflex over (p)}n) n-dimension position; lets {circumflex over (d)}i=┌(pi−{dot over (b)}i)/bi┐+┌(di−pi+{dot over (b)}i┐, and {circumflex over (p)}=|(pi−{dot over (b)}i)/bi|+1, 1≦i≦n;
Â{circumflex over (d)}ip, 1≦i≦n, expresses a series of n−1 dimensional binary matrixes
on {circumflex over (d)}i axis in order, wherein
represents the original matrix at {circumflex over (p)}i position, and
expresses a zero matrix filling at {circumflex over (p)}i position.
10. The cryptographic method according to claim 7 , further including a password, wherein said password has at least one variable data, said data read by said module, each including: (p1, p2, . . . pn) and/or d1×d2× . . . ×dn and/or ({dot over (s)}1, {dot over (s)}2, . . . {dot over (s)}n) and/or s1×s2× . . . ×sn and/or S and/or ({dot over (b)}1, {dot over (b)}2, . . . , {dot over (b)}n) and/or b1×b2× . . . ×bn and/or Y and/or TE1 and/or TD1 and/or TE2 and/or TD2.
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